I see your point.
Although I pretty much leave my laptop, or my desktop when I had one, on 24/7. And with iTunes, they are already preset and categorized by genre so there are 100s of stations for all tastes. So with literally 3 taps of my trackpad, I'm rocking.
I wouldn't even know where to start looking for web addresses of internet stations...
Check out Radio Paradise though... it's in the eclectic section.. or .com.
...if you can't find a stand alone player, you have options.